Oct 29 (Reuters) - Johnson Controls International Plc is nearing a deal to sell its power solutions business, which makes car batteries, to Brookfield Asset Management Inc for between $13 billion and $14 billion, people familiar with the matter said on Monday.

The transaction would be one of the largest leveraged buy-outs this year and allow Johnson Controls to focus on its building technologies and solutions business, which makes heating, ventilation and air conditioning systems, as well as building access control and fire detection systems.

Brookfield, an investment firm with over $285 billion in assets under management, outbid buyout firm Apollo Global Management LLC in an auction for the power solutions unit, the sources said.

Brookfield and Johnson Controls could finalize the terms of a deal for the unit, whose batteries are used in about a third of cars globally, as early as this week, the sources said, though they noted there was always a chance the negotiations could end unsuccessfully.

The sources asked not to be identified because the matter is confidential. Brookfield and Apollo declined to comment, while Johnson Controls did not immediately respond to a request for comment. Bloomberg News reported earlier that Brookfield was nearing a deal for Johnson Controls' auto battery business, which includes the Varta, Heliar, LTH, MAC, Optima and Delkor brands.

Johnson Controls shares were up 1.3 percent at $31.72 in afternoon trading in New York, giving the company a market capitalization of more than $29 billion.

The deal would represent the biggest shake-up at Johnson Controls since its merger in 2016 with Tyco International.

Johnson Controls' power solutions business, which produces and distributes about 154 million lead-acid batteries for passenger cars and light trucks annually, carries higher margins but has been capital intensive for Johnson Controls, analysts have said.

More deals in the sector are likely, as industrial conglomerates continue to separate businesses that are too disparate in terms of financial performance. United Technologies Corp is currently weighing a three-way split among its Carrier air conditioner business, its Otis elevator business, and its aerospace division, which makes Pratt & Whitney jet engines.

Earlier on Monday, Honeywell International Inc completed a spin-off of its residential solutions business, Resideo Technologies Inc, after spinning off its Garrett Motion Inc transportation systems business earlier this month. (Reporting by Harry Brumpton and Joshua Franklin in New York; Editing by Dan Grebler)